Math has a bad rap, writes math professor Manil Suri in a recent New York Times op-ed, and would be better geared to students as a playful and stimulating subject of ideas. Unfortunately, that’s not at all what our culture currently embraces.

“Sadly, few avenues exist in our society to expose us to mathematical beauty,” Suri writes. “In schools, as I’ve heard several teachers lament, the opportunity to immerse students in interesting mathematical ideas is usually jettisoned to make more time for testing and arithmetic drills. The subject rarely appears in the news media or the cultural arena.”

While research suggests that improving self-efficacy and providing math-positive role models can help spark interest and stave off math anxiety, what some mathematicians and teachers are looking for reaches beyond surviving or tolerating math class, but helping connect students to mathematics beauty. Suri wants students to “fall in love” with math, and suggests that maybe our entire approach to math is upside down, and deserves to be righted.

But how does a person fall in love with math? For too many, math class conjures up anxious worksheets filled with rows of unanswered problems. Students go along, seeming to perform the steps required — plug in the formulas, solve for x — without ever understanding what they’re doing, or why.

“We have defined math rather narrowly in the U.S. to mean memorizing procedures and performing them accurately and quickly.”

Cornell Math Professor and New York Times columnist Steven Strogatz, author of The Joy of x, said much of middle and high school math curriculum (which covers not basic arithmetic, but higher math) doesn’t appeal to students’ hearts, instead offering answers to questions that kids would never ask — which he calls “the definition of boredom.”

“When people want to learn about music, they’ve reacted to it, they love it and naturally want to learn more about it. They have their own questions,” Strogatz said. When introducing higher math to a group of curious young students, he suggests first “showing them math’s greatest hits” and allowing them to become fascinated; students then naturally come up with their own questions. Suri was on the right track, Strogatz said, when he suggested students learn something like the origin of numbers — because the first step is falling in love with the mathematical ideas behind the formulas and procedures.

Strogatz acknowledges that grasping the concepts of higher math can pave the way to many wonderful careers — many in the popular and highly needed STEM fields. But rationalizing to students that math improves reasoning skills or that “you’ll need it in the real world” are two strategies doomed to fail, he said, because they not-so-subtly suggest that math isn’t worth learning for its own sake, but parallels something more akin to “mental push-ups.”

“Have you ever asked why you need music?” Strogatz said. “You don’t need music. It’s nice to know about music. Why do you need to look at Picasso?” Perhaps when presented first as the story of how the universe works, math can become beautiful.

Grabbing students’ hearts, however, is only the first step to falling in love with math. High school math teacher Dan Meyer realized his algebra classes needed a makeover, the subject of an inspiring TED talk in which Meyer takes a larger look at how math is taught. “We have defined math rather narrowly in the U.S. to mean memorizing procedures and performing them accurately and quickly,” he said. “Those are certainly important parts of mathematics, but they aren’t the only parts, or even the most important parts. We need to define math to include skills like prediction, argumentation, and systematic thinking. These are important skills to have whether you go into a STEM field or not.”

Instead of trying to make math less boring by inserting more interesting, youthful details, said Meyer, like “‘Justin Bieber’ or loosely pasting real-world contexts into word problems from the 1960s,” math needs to be accessible far more than it needs to be relevant. One large part of providing access to math concepts, he said, is helping students understand that math makes sense with or without the teacher, and that students can create and solve new problems without a textbook.

But would he go so far to try and convince his high school students that math is beautiful? “Math involves creation,” Meyer said. “You can add up different sets of numbers or attach different kinds of shapes together and create theories about the patterns you’re seeing. Math is personal. Those theories and how you express them is personal to you. ‘Beautiful’ is the sort of word that makes a lot of people who do math for a living seem crazy to those who don’t, but when you’re creating something that’s personal to you, I suppose that’s rather beautiful.”

Our (U.S) cultural tendencies, along with an overwhelming majority of the populace that was educated under an educational system that currently doesn’t relate to the learning needs of students, has elevated mathematical non-proficiency to a modern badge of honor. This seems like much more of an issue than curricula or its pedagogical implementations.

Zeph

This is not only true for those who don’t love math, but even for those who do. Because you grow up loving math but you don’t know what to do with it, is it just a tool? Or just something to help you get into professional degree programs? As someone who has always loved math, I would have actually liked to learn math for learning’s sake when I was younger…these things prof.dan talks about – via music, art…even if I used to create art all the time. This isn’t unique to US, as prof. suri stated – it’s rather universal and with the recent access to internet, I’m sure kids are growing up in much different milieu than I did.

Sheryl Morris

Michael S. Schneider’s work “A Beginner’s Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science: A Voyage From 1 to 10” gave me new interest in the relationships among numbers, geometric shapes, and patterns.
I was compelled to design a guide to help others bring a sense of wonder and curiosity to young children. Find “SNAP Scaffolding for Numerical Synapses” at Amazon.

I have taught math for 24 years to primary school students and when you relate it to the real world, and tell them stories of origins and ask them to find numbers or patterns all around them, it becomes meaningful and they feel motivated. They need to explore and not memorize.

Really, really, really nice idea. Most instructional materials, however, shove this under a bus wheel, even while giving lip service to learnign concepts and appreciating beauty. A particularly painful example of this is the over-touted Khan Academy, with its procedural focus (with all kinds of errors) and “you just have to practice more!” approach to understanding concepts. Show me the materials that teach conceptually, please! (Here comes the silence…)

Tommie

I hear your frustration, Susan. Check out http://www.cpm.org for a curricula written by teachers that stresses understanding the concepts but doesn’t throw out the need to know some skills. CPM is a non profit, not part of any of the big publishers just looking at the bottom line. Also, whenever anyone praises the Khan Academy, I show them this video. About 11 – 12 minutes long, but so worth it.

Susan Jones

I won third prize in the contest that video won, so I’m familiar with it 🙂 However, it doesn’t convince people.
I like a lot of what Annenberg puts out (and I often refer people to their site for evidence that cranking out problems doesn’t work, to that great video about the Ivy League grads who don’t understand the actual application of what photosynthesis means… that yes, plants turn *air* into wood; it doesn’t come from the dirt or the sun…)

HighSchooler

I think that (at least a proper subset of) the praises for Khan Academy are exactly because they allow a students to learn conceptually the idea behind the problem before doing it (and as they detestably say at my school: plugging and chugging), furthermore Sal can pose a problem such as that shown in the above linked video (i.e from the Japanese classroom) and the student can pause and try to solve it, something that is completely unavailable in the traditional American classroom. Sal seems to have an intuitionist attitude about pedagogy, which is opposed to the “plug in numbers to formulae” approach most American teachers have, and while I will concede that this method of instruction might not be the most effective (I long for the day my classroom teachers will give us a challenging problem to solve on our own), I think it must be said that it is better than solely the classroom approach. I personally do tout Khan Academy because of its ability to introduce me to the conceptual mathematical basics from which I can draw when solving harder and more interesting problems. I think it would be a gross misuse of Khan Academy as simply an end to education, since it is designed (and better suited) as a means to provide a basic intuitive framework from which the necessary mathematical reasoning can be built.

Actually, I’m skeptical about there being much out there that really “teaches conceptually.” In the end, getting at concepts as a significant piece of the math pie requires skilled teachers who are deeply committed to helping students by problematizing math in ways that invites and demands real mathematical thinking. It’s hard as hell to do that in a textbook and actually get it published. Leave too much out and teachers, parents, and students bitch like little whining babies. Put too much in and you guarantee that any impetus to really engage in productive struggle with problems and ideas will wither on the vine. Takes a teacher with a fine sense of subtlety to know when to offer a bit of a hint, a question that leads, but not too much, or helps students see that they’re stuck and how they might back away and try something else. Bob and Ellen Kaplan of the Math Circle in Cambridge, MA are the most adept at this I’ve ever seen, and frankly I don’t think it’s materials that do the teaching for them.

This paper speaks from my heart. I try everywhere to spread the beauty of Math, whenever I can. We made for this purpose also animated movies about math, which can in a very quick an popular way to start or provoke some deep questions and interests in math. Here is a trailer to our movies : http://www.youtube.com/watch?v=nWW3tCx45cI&feature=youtu.be,

Chad P.

I think another way of looking at math, especially at a rudimentary level is to have fun practicing it. Here’s a great example: prodigygame.com/

I care about this topic very much, and see it lamented often. However, no one ever seems to provide a thorough or practical solution. All I tend to collect from these conversations are a few gems in the comments sections from folks sharing links or books. It just feels like the solution is to now teach math in hodge-podge way using these (albeit, good) resources. Maybe that’s a good solution, but if it’s not, how are teachers really supposed to approach their teaching in any kind of systematic way?

I remember when my kids were at Montessori school, and I went to a talk for parents about some of the things they were learning. The purpose of the Pythagorean Theorum was explained, using the historical context and a hands-on demonstrative aid that showed it in concrete terms. My only exposure to it before had been in a typical highschool math class, where it was presented as a formula and followed up with pages of practice problems. I felt a light come on and an excitement about math that I never experienced when I slogged through it in my school days.

I now homeschool my children (Montessori didn’t work for other reasons), and I make sure that we spend lots of time on the beauty of math. There are many DVD’s, videos, books, etc. that do just that. The music analogy is perfect — what’s the point of learning just the notes, without ever having heard the orchestra?

Author

Holly Korbey

Holly Korbey’s work on parenting and education has appeared in The New York Times, The Atlantic, Babble, Brain, Child Magazine, and others. She lives in Nashville with her family. Follow her on Twitter: @HKorbey